Electrodiffusion model simulation of rectangular current pulses in a voltage-biased biological channel

Carl L. Gardner; Joseph W. Jerome; Robert S. Eisenberg

doi:10.1006/jtbi.2002.3123

Electrodiffusion model simulation of rectangular current pulses in a voltage-biased biological channel

Carl L. Gardner^*, Joseph W. Jerome, Robert S. Eisenberg

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poisson's equation, depending on the choice of boundary conditions. The TRBDF2 method is employed for the advection-diffusion equation. The rectangular wave shape of previously simulated traveling wave current pulses is preserved by the full set of partial differential equations for electrodiffusion.

Original language	English (US)
Pages (from-to)	291-299
Number of pages	9
Journal	Journal of Theoretical Biology
Volume	219
Issue number	3
DOIs	https://doi.org/10.1006/jtbi.2002.3123
State	Published - 2002

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

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10.1006/jtbi.2002.3123

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title = "Electrodiffusion model simulation of rectangular current pulses in a voltage-biased biological channel",

abstract = "Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poisson's equation, depending on the choice of boundary conditions. The TRBDF2 method is employed for the advection-diffusion equation. The rectangular wave shape of previously simulated traveling wave current pulses is preserved by the full set of partial differential equations for electrodiffusion.",

author = "Gardner, {Carl L.} and Jerome, {Joseph W.} and Eisenberg, {Robert S.}",

note = "Funding Information: *Corresponding author. Tel.: +1-480-965-0226; fax: +1-480-965-0461. E-mail addresses: gardner@asu.edu (C. L. Gardner), jwj@math.nwu.edu (J. W. Jerome), beisenbe@rush.edu (R. S. Eisenberg). z Research supported in part by the National Science Foundation under Grant DMS-9706792 and by DARPA under Grant N65236-98-1-5409. 8 Research supported in part by the National Science Foundation under Grant DMS-9704458. ** Research supported in part by DARPA under Grant N65236-98-1-5409.",

year = "2002",

doi = "10.1006/jtbi.2002.3123",

language = "English (US)",

volume = "219",

pages = "291--299",

journal = "Journal of Theoretical Biology",

issn = "0022-5193",

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AU - Gardner, Carl L.

AU - Jerome, Joseph W.

AU - Eisenberg, Robert S.

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PY - 2002

Y1 - 2002

N2 - Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poisson's equation, depending on the choice of boundary conditions. The TRBDF2 method is employed for the advection-diffusion equation. The rectangular wave shape of previously simulated traveling wave current pulses is preserved by the full set of partial differential equations for electrodiffusion.

AB - Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poisson's equation, depending on the choice of boundary conditions. The TRBDF2 method is employed for the advection-diffusion equation. The rectangular wave shape of previously simulated traveling wave current pulses is preserved by the full set of partial differential equations for electrodiffusion.

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Electrodiffusion model simulation of rectangular current pulses in a voltage-biased biological channel

Abstract

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